Mathematics - Quadratic Equation Question with Solution | TestHub

$P\left(x\right)=a{x}^2+b$with a, b of same sign.
$P \left(P\left(x\right)\right)=a{\left(a{x}^2+b\right)}^2+b$
If$x ϵ R or ix ϵ R$
$\Rightarrow x^2 ϵ R$
$\Rightarrow P\left(x\right)ϵ R$
$\Rightarrow P\left(P\left(x\right)\right)\ne 0$
Hence real or purely imaginary number can not satisfy$P \left(P\left(x\right)\right)=0$